Yes and No.
Yes - To connect to a DB, you can either have a DSN or DSN-less connection. DSN requires you to set it up on the server ahead of time. DSN-less creates the connection to the DB on the fly from the ASP code.
No - You cannot have ASP without IIS (well, there are some offshoots of IIS.. chilisoft, or something, has an ASP-like language, but I'm not familiar with it). Without it you're not gonna get anything. IIS receives the request for a page, checks to see if it's there, checks its security, executes the code for it, then serves the results back to the client. But IIS is not required for a dynamic website. There are other web servers such as Apachi, WebLogic, WebSphere, and many more, but ASP is pretty much unique to IIS.